Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations x-y+4z=23 2x-y+z=-1 6x+4y+2y=-44

I assume the third equation is supposed to be . We can divide both sides by 2 right away to simplify it a bit, .

To start, the system in augmented-matrix form is

Subtract 2 times row 1 from row 2, and 3 times row 1 from row 3:

Subtract 5 times row 2 from row 3:

Multiply row 3 by 1/24:

Add 7 times row 3 to row 2:

Add row 2 and -4 times row 3 to row 1:

Then the solution to the system is

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (: